Print instrument name of staff whose empty section from the start was removed with RemoveAllEmptyStaves

[Eirik B]

Hi all,
When engraving music where an instrument comes in later in the piece, I 
normally prefer to remove its empty staves using RemoveAllEmptyStaves within 
the Staff context. When doing so, the instrument name is not printed when the 
staff becomes visible later in the piece.
Is there a way to (i) give the entire staff a new indent similar to the indent 
at the start of the piece (to accommodate space for the instrument name) and 
(ii) print the instrument name on the staff when it first becomes visible?
I am aware that I could use shortInstrumentName to print the instrument name on 
all staffs, but I am only interested in printing the instrument name only on 
the first staff of an instrument when it first becomes visible in the piece.
See below MWE showing that although the instrument name is given, it is not 
printed on a staff whose start was removed with RemoveAllEmptyStaves
Please also note that I have asked this question on music StackExchange 
https://music.stackexchange.com/questions/142858/print-instrument-name-of-staff-whose-empty-section-from-the-start-was-removed-wi.

\version "2.24.4"
soloVoice = {\repeat unfold 20 d1}
instrumentVoice = {R1*10 \break \repeat unfold 10 d1}

\score {
  <<
    \new Staff
    \with {
      instrumentName = "Soloist"
    }
    <<
      \soloVoice
    >>
    \new Staff
    \with {
      instrumentName = "Instrument"
    }
    <<
      \instrumentVoice
    >>
  >>
  \layout {
    \context {
      \Staff \RemoveAllEmptyStaves
    }
  }
}


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